Method for designing a filter system

ABSTRACT

The filter system designed according to the inventive method comprises at least two longitudinal branches with longitudinal inductive resistors and at least one filter step (B), and an adjacent filter step (A). The filter step (B) is provided with at least one transverse branch that is interposed in between the longitudinal branches, the adjacent filter step (A) directly adjoining the transverse branch. The umber of inductive resistors of a filter step that are wound around different magnet cores can be reduced by equivalence transformation.

[0001] Design of a filter system with at least two longitudinal branches that have longitudinal inductors, and a filter arrangement with at least one filter step that has at least one transverse branch interposed between the longitudinal branches and at least one adjacent filter step that directly adjoins the transverse branch.

[0002] Such a filter system, which is suitable as a low-pass filter for an ADSL diplexer, is known from the “Handbook of Filter Synthesis” by Anatol I. Zverev, 1967, e.g., p. 59, FIG. 2.39.

[0003] A filter system with four connections has two longitudinal branches, which are symmetrically constructed. The filter system has a plurality of filter steps connected in series. The first filter step on the input side has one longitudinal inductor per longitudinal branch. The remaining filter steps, on the input side, each have a transverse branch comprising a capacitor interposed between two coupled transverse inductors and, on the output side, one longitudinal inductor per longitudinal branch. The longitudinal inductors and the transverse inductors of each filter step are coupled with each other, i.e., the inductors consist of windings that are wound around the same magnetic core. These magnetic cores are particularly costly. For each additional filter step, two additional magnetic cores are required. The more filter steps the filter system has, the more expensive it is.

[0004] In the older German Patent Application 198 51 872.2, to increase the return loss, each longitudinal inductor is replaced by two longitudinal inductors that are connected in series and are not coupled with each other. An electrical resistor is connected in parallel to one of the longitudinal inductors. This does not substantially change the transmission characteristics, such as group delay distortion.

[0005] The object of the invention is to define a method for designing a filter system, in which the filter system has fewer magnetic cores compared to the prior art, without changing the transmission characteristics.

[0006] This object is attained by a method according to Claim 1, 2 or 3. Embodiments and further developments of the inventive concept are set forth in the dependent claims.

[0007] The method according to the invention for designing a filter system with at least two longitudinal branches that have longitudinal inductors, at least one filter step that is provided with at least one transverse branch interposed between the longitudinal branches, and at least one adjacent filter step, which directly adjoins the transverse branch, determines the arrangement of the inductors by means of a first type of transformation characterized by the following process steps:

[0008] First, the filter step has at least one free longitudinal inductor of the first longitudinal branch, a free longitudinal inductor of the second longitudinal branch coupled therewith and the transverse branch which consists of a capacitor that is interposed between two transverse inductors that are coupled together. The adjacent filter step first has at least one free longitudinal inductor of the first longitudinal branch and a free longitudinal inductor of the second longitudinal branch coupled therewith.

[0009] Subsequently, between the transverse branch and the adjacent filter step, a preliminary longitudinal inductor and a compensation inductor compensating the same and connected in series are inserted in each longitudinal branch. The preliminary longitudinal inductors are coupled with each other and the compensation inductors are coupled with each other.

[0010] Subsequently the compensation inductors are integrated into the free longitudinal inductors of the adjacent filter step.

[0011] Afterwards, the preliminary longitudinal inductors, the free longitudinal inductors of the filter step and the transverse inductors are replaced by four end inductors coupled with each other such that an equivalent circuit diagram of the four end inductors corresponds with the circuit diagram of the preliminary longitudinal inductors, the free longitudinal inductors of the filter step and the transverse inductors.

[0012] A second type of transformation provides for the following process steps:

[0013] First, the filter step has a longitudinal inductor of the first longitudinal branch, a longitudinal inductor of the second longitudinal branch coupled therewith and the transverse branch. The adjacent filter step first has at least one longitudinal inductor of the first longitudinal branch and a longitudinal inductor of the second longitudinal branch coupled therewith.

[0014] Subsequently, the longitudinal inductors of the filter step are each replaced by a first longitudinal inductor, which forms at least one part of the free longitudinal inductor, and a second longitudinal inductor connected in series therewith, to which a resistor R is connected in parallel. Corresponding longitudinal inductors belonging to the same filter step are coupled with each other.

[0015] Then, the preliminary longitudinal inductor and the compensation inductor are inserted.

[0016] A third type of transformation provides for the following process steps:

[0017] First, the filter step has a longitudinal inductor of the first longitudinal branch, a longitudinal inductor of the second longitudinal branch coupled therewith and the transverse branch. The adjacent filter step first has at least one longitudinal inductor of the first longitudinal branch and a longitudinal inductor of the second longitudinal branch coupled therewith.

[0018] Subsequently, the longitudinal inductors of the filter step and the adjacent filter step are replaced, respectively, by a first longitudinal inductor and a second longitudinal inductor connected in series therewith, to which a resistor is connected in parallel. Corresponding longitudinal inductors that belong to the same filter step are coupled with each other.

[0019] Subsequently, the first longitudinal inductors and the second longitudinal inductors of the same filter step per longitudinal branch are replaced by a new first longitudinal inductor and a new second longitudinal inductor such that the new second longitudinal inductor is connected in series with the resistor. This series connection is connected in parallel to the new first longitudinal inductor. In the same filter step, the new first longitudinal inductors of the first longitudinal branch and the second longitudinal branch are coupled with each other and the new second longitudinal inductors of the first longitudinal branch and the second longitudinal branch are coupled with each other.

[0020] Afterwards, in each longitudinal branch of the filter step, an additional preliminary longitudinal inductor and an additional compensation inductor compensating the same and forming at least a portion of the free longitudinal inductor are inserted between the parallel connection of the new first longitudinal inductor to the series connection and the adjacent filter step.

[0021] Thereafter, the additional preliminary longitudinal inductors, the new first longitudinal inductors which form an additional circuit diagram, are replaced by four longitudinal end inductors that are coupled with each other, such that an equivalent circuit diagram of the four longitudinal end inductors corresponds with the additional circuit diagram.

[0022] Then, the preliminary longitudinal inductor and the compensation inductor are inserted.

[0023] A further embodiment of the invention provides for a method in which a first capacitor electrode of the capacitor is connected with a first end inductor that is connected with the adjacent filter step and with a second end inductor,

[0024] in which the winding direction of the first inductor relative to the capacitor corresponds with the winding direction of the second end inductor relative to the capacitor,

[0025] in which a second capacitor electrode of the capacitor is connected with a third end inductor that is connected with the adjacent filter step and with a fourth end inductor,

[0026] in which the winding direction of the first end inductor relative to the capacitor is opposite to the winding direction of the third end inductor relative to the capacitor,

[0027] in which the winding direction of the third end inductor relative to the capacitor corresponds with the winding direction of the fourth end inductor relative to the capacitor.

[0028] In addition, the method according to the invention can be further developed in that

[0029] a first capacitor electrode of the capacitor is connected with a first end inductor, which is connected with the adjacent filter step,

[0030] a second end inductor is connected with the first end inductor and with the adjacent filter step,

[0031] the winding direction of the first end inductor relative to a first reference point on the electrical connection between the first end inductor and the second end inductor is opposite to the winding direction of the second end inductor relative to the first reference point,

[0032] a second capacitor electrode of the capacitor is connected with a third end inductor, which is connected with the adjacent filter step,

[0033] a fourth end inductor is connected with the third end inductor and with the adjacent filter step,

[0034] the winding direction of the third end inductor relative to a second reference point on the electrical connection between the third end inductor and the fourth end inductor is opposite to the winding direction of the fourth end inductor relative to the second reference point,

[0035] the winding direction of the first end inductor relative to the capacitor is opposite to the winding direction of the third end inductor relative to the capacitor.

[0036] Furthermore it may be provided that

[0037] a first capacitor electrode of the capacitor is connected with a second end inductor,

[0038] in which the second end inductor is connected with a first end inductor which is connected with the adjacent filter step,

[0039] the winding direction of the first end inductor relative to a seventh reference point on the electrical connection between the first end inductor and the second end inductor is opposite to the winding direction of the second end inductor relative to the seventh reference point,

[0040] a second capacitor electrode of the capacitor is connected with a fourth end inductor,

[0041] the fourth end inductor is connected with a third end inductor which is connected with the adjacent filter step,

[0042] the winding direction of the third end inductor relative to a ninth reference point on the electrical connection between the third end inductor and the fourth end inductor is opposite to the winding direction of the fourth end inductor relative to the ninth reference point, and

[0043] the winding direction of the first end inductor relative to the capacitor is opposite to the winding direction of the third end inductor relative to the capacitor.

[0044] Another further development provides that

[0045] a first longitudinal end inductor is connected in series with the resistor of the filter step in the first longitudinal branch, and a second longitudinal end inductor is connected in parallel to this series connection,

[0046] The winding direction of the first longitudinal end inductor relative to a third reference point on the electrical connection between the first longitudinal end inductor and the second longitudinal end inductor is opposite to the winding direction of the second longitudinal end inductor relative to the third reference point,

[0047] a third longitudinal end inductor is connected in series with resistor R of the filter step in the second longitudinal branch and a fourth longitudinal end inductor is connected in parallel to this series connection,

[0048] the winding direction of the third longitudinal end inductor relative to a fourth reference point on the electrical connection is between the third longitudinal end inductor and the fourth longitudinal end inductor relative to the fourth reference point,

[0049] the winding direction of the first longitudinal end inductor relative to the transverse branch is opposite to the winding direction of the third longitudinal end inductor relative to the transverse branch.

[0050] Alternatively, it may be provided that

[0051] a first longitudinal end inductor is connected in series with a second longitudinal end inductor to which resistor R of the filter step in the first longitudinal branch is connected in parallel,

[0052] the winding direction of the first longitudinal end inductor relative to a fifth reference point on the electrical connection between the first longitudinal end inductor and the second longitudinal end inductor corresponds with the winding direction of the second longitudinal end inductor relative to the fifth reference point,

[0053] a third longitudinal end inductor with a fourth longitudinal end inductor to which the resistor of the filter step in the second longitudinal branch is connected in parallel,

[0054] the winding direction of the third longitudinal end inductor relative to a sixth reference point on the electrical connection between the third longitudinal end inductor and the fourth longitudinal end inductor corresponds with the winding direction of the fourth longitudinal end inductor relative to the sixth reference point,

[0055] the winding direction of the first longitudinal end inductor relative to the transverse branch is opposite to the winding direction of the third longitudinal end inductor relative to the transverse branch.

[0056] Another alternative is characterized in that

[0057] a second longitudinal end inductor and a resistor of the filter step in the first longitudinal branch are connected in series,

[0058] in which an electrical connection is connected in parallel to the series connection comprised of the second longitudinal end inductor and the resistor,

[0059] a first longitudinal end inductor is interposed between the adjacent filter step and the series connection comprised of the second longitudinal end inductor and the resistor,

[0060] the winding direction of the first longitudinal end inductor relative to an eighth reference point on the electrical connection between the first longitudinal end inductor and the second longitudinal end inductor corresponds with the winding direction of the second longitudinal end inductor relative to the eight reference point,

[0061] a fourth longitudinal end inductor and a resistor of the filter step in the first longitudinal branch are connected in series, in which an electrical connection is connected in parallel to the series connection comprising the fourth longitudinal end inductor and the resistor,

[0062] a third longitudinal end inductor is interposed between the adjacent filter step and the series connection comprised of the fourth longitudinal end inductor and the resistor,

[0063] the winding direction of the third longitudinal end inductor relative to a tenth reference point on the electrical connection between the third longitudinal end inductor and the fourth longitudinal end inductor corresponds with the winding direction of the fourth longitudinal end inductor relative to the tenth reference point, and

[0064] the winding direction of the first longitudinal end inductor relative to the transverse branch is opposite to the winding direction of the third longitudinal end inductor relative to the transverse branch.

[0065] Finally, one embodiment of the invention may consist in that

[0066] at least one additional filter step adjacent to the filter step is provided, and

[0067] the compensation inductor for the transformation of the additional adjacent filter step are integrated into the free longitudinal inductors of the filter step.

[0068] Accordingly, the procedure should, for example, be as follows. First, the filter step has at least one free longitudinal inductor of the first longitudinal branch, a free longitudinal inductor of the second longitudinal branch coupled therewith, and the transverse branch, which consists of a capacitor interposed between two transverse inductors which are coupled with each other. The term “free longitudinal inductor” denotes a longitudinal inductor to which no additional component is connected in parallel. The adjacent filter step first has at least one free longitudinal inductor of the first longitudinal branch and a free longitudinal inductor of the second longitudinal branch coupled therewith. This initial state corresponds to a filter arrangement of the prior art. For transformation, a preliminary longitudinal inductor and a compensation inductor compensating the same and connected in series therewith are then inserted into each longitudinal branch between the transverse branch and the adjacent filter step. The preliminary inductors are coupled with each other and the compensation inductors are also coupled with each other. The circuit characteristics of the filter system thus transformed remain the same, since the preliminary longitudinal inductor is compensated by the compensation inductor. For further transformation, the compensation inductors are then integrated into the free longitudinal inductors of the adjacent filter step. Thereafter, the preliminary longitudinal inductors, the free longitudinal inductors of the filter step, and the transverse inductors are replaced by four end inductors that are coupled with each other such that an equivalent circuit diagram of the four end inductors corresponds with the circuit diagram of the preliminary longitudinal inductors, the free longitudinal inductors of the filter step and the transverse inductors.

[0069] Since the four end inductors are coupled with each other, said four end inductors consist of windings that are wound around the same magnetic core.

[0070] The described transformation makes it possible to save one magnetic core for each filter step that has a transverse branch, since the free inductors and the transverse inductors, for which the two magnetic cores are required, are transformed in such a way that only one magnetic core is required.

[0071] The described transformation is an equivalence transformation, so that the circuit characteristics of the filter configuration, such as group delay distortion and transfer function, are preserved in the transformation.

[0072] A filter system designed according to the invention consequently has fewer magnetic cores compared to the prior art without any change in the circuit characteristics of the filter system.

[0073] The transformation will now be described in greater detail. The longitudinal branches of a filter system are typically arranged in pairs and symmetrical to each other, with corresponding inductors of the longitudinal branches of a pair being coupled to each other. Due to this symmetrical construction, it is sufficient to look at only one longitudinal branch when describing the transformation:

[0074] Three transformed basic circuits are depicted in FIGS. 1a, 1 b and 1 c. They have the same equivalent circuit diagram, which is shown in FIG. 2a.

[0075] The equivalent circuit diagram shown in FIG. 2a corresponds to a portion of a filter arrangement according to the prior art, in which the preliminary inductor L_(V) has been inserted. The preliminary inductor L_(V) is connected with the free longitudinal inductor L_(F) and the transverse inductor L_(Q). From this equivalent circuit diagram, with suitable transformation, one obtains the three transformed basic circuits. Each of the basic circuits comprises two inductors that are coupled with each other. The coupling in FIGS. 1a, 1 b, 1 c is made clear by the framing of the inductors that are coupled with each other. For the transformation, the value of the preliminary longitudinal inductor L_(V) has to obey the following equation: $L_{v} = {- \frac{L_{F} \cdot L_{Q}}{L_{F} + L_{Q}}}$

[0076] In a filter arrangement according to the prior art, each filter step per longitudinal branch has only the free longitudinal inductor L_(F). Consequently, to realize the equivalent circuit diagram, the preliminary longitudinal inductor L_(V) must be inserted. To preserve the circuit characteristics, a compensation inductor L_(K) compensating said preliminary longitudinal inductor L_(V) must therefore also be inserted. For the sake of clarity, capacitor K of the transverse branch is also depicted in FIG. 2b. That is depicted in FIG. 2b. The following applies:

L _(V) =−L _(K)

[0077] In a transformation of the equivalent circuit diagram depicted in FIG. 2b relative to the basic circuit depicted in FIG. 1a, one obtains the circuit diagram shown in FIG. 3a. This transformation is hereinafter referred to as the first transformation. The compensation inductor L_(K) requires no additional magnetic core, since due to the series connection with the free longitudinal inductor of the adjacent filter step, it can be integrated into the free longitudinal inductor of the adjacent filter step, i.e., it can be combined into a single inductor. Since only the transformation of one longitudinal branch was depicted, only two of the four end inductors are shown in FIG. 3a.

[0078] The capacitor K is connected with a first end inductor L_(E)(1), which is connected with the adjacent filter step, and with a second end inductor L_(E)(2). The fact that the two end inductors are distinguished by (1) and (2) and not by the index makes it clear that the two end inductors L_(E)(1), L_(E)(2) are different inductors but that they are coupled with each other. The following applies: ${L_{E}(1)} = \frac{L_{Q}^{2}}{L_{F} + L_{Q}}$

 L _(E) (2)=L _(F) +L _(Q)

[0079] The winding direction of the first end inductor L_(E)(1) relative to the capacitor K corresponds with the winding direction of the second end inductor L_(E)(2) relative to the capacitor K. This is represented by the dots on the end inductors L_(E)(1), L_(E)(2). Instead of both being at the top, the dots can also both be at the bottom. The absolute winding direction is not important, only the winding directions relative to each other.

[0080] The longitudinal branches of a pair are symmetrically constructed in such a way that the winding direction of the first end inductor L_(E)(1) relative to the capacitor K is opposite to the winding direction of a third end inductor, which corresponds with the first end inductor L_(E)(1), relative to the capacitor K.

[0081] In a transformation based on the equivalent circuit diagram depicted in FIG. 2b relative to the basic circuit shown in FIG. 1b, the circuit diagram depicted in FIG. 3b is obtained. This transformation is hereinafter referred to as the second transformation. The capacitor K is connected with the first end inductor L_(E)(1′), which is connected with the adjacent filter step. The second end inductor L_(E)(2′) is connected with the first end inductor L_(E)(1′) and with the adjacent filter step but not with the capacitor K. The following applies: ${L_{E}\left( 1^{\prime} \right)} = \frac{L_{Q}^{2}}{L_{F} + L_{Q}}$ ${L_{E}\left( 2^{\prime} \right)} = \frac{L_{F}^{2}}{L_{F} + L_{Q}}$

[0082] The winding direction of the first end inductor L_(E)(1′) relative to a first reference point 1 on the electrical connection between the first end inductor L_(E)(1′) and the second end inductor L_(E)(2′) is opposite to the winding direction of the second end inductor L_(E)(2′) relative to the first reference point 1. The winding directions are again indicated by the dots on the end inductors L_(E)(1′), L_(E)(2′). Here, too, only the relative winding directions are important, i.e., the dot on the first end inductor L_(E)(1′) can be at the bottom instead of the top if the dot in the second end inductor L_(E)(2′) is to the left instead of to the right.

[0083] The longitudinal branches of a pair are constructed symmetrically to each other such that the winding direction of the first end inductor L_(E)(1′) relative to the capacitor K is opposite to the winding direction of a third end inductor that corresponds to the first end inductor relative to the capacitor K.

[0084] In a transformation based on the equivalent circuit diagram shown in FIG. 2b relative to the third basic circuit depicted in FIG. 1c, the circuit diagram shown in FIG. 3c is obtained. This transformation is hereinafter referred to as the third transformation. The capacitor K is connected with the second end inductor L_(E)(2″). The second end inductor L_(E)(2″) is connected with the first end inductor L_(E)(1″), which is connected with the adjacent filter step. The following applies: ${L_{E}\left( 1^{''} \right)} = \frac{L_{F}^{2}}{L_{F} + L_{Q}}$

 L _(E) (2″)=L _(F) +L _(Q)

[0085] The winding direction of the first end inductor L_(E)(1″) relative to a seventh reference point 7 on the electrical connection between the first end inductor L_(E)(1″) and the second end inductor L_(E)(2″) is opposite to the winding direction of the second end inductor L_(E)(2″) relative to the seventh reference point 7. The winding directions are again indicated by means of dots on the end inductors L_(E)(1″), L_(E)(2″). Here, too, only the relative winding direction is important, i.e., the dot on the first end inductor L_(E)(1″) can be on the left instead of the right if the dot on the second end inductor L_(E)(2″) is at the top instead of at the bottom.

[0086] To increase the return loss of the filter system, it is advantageous to replace a longitudinal inductor L of the first longitudinal branch and a longitudinal inductor of the second longitudinal branch of the same filter step coupled therewith by, respectively, a first longitudinal inductor L₁ and a second longitudinal inductor L₂ connected in series therewith, to which a resistor R is connected in parallel. The corresponding longitudinal inductors that belong to the same filter step are coupled with each other (see FIG. 4). Thus, the two first longitudinal inductors L₁ are coupled with each other and the two second longitudinal inductors L₂ are coupled with each other. This passive transformation makes it possible to adapt the filter configuration to a complex terminating resistor, so that the return loss is significantly increased compared to a filter system without passive transformation.

[0087] Without passive transformation, the free longitudinal inductor L_(F) is, for example, equal to the longitudinal inductor L.

[0088] With passive transformation, the free longitudinal inductor L_(F) is, for example, the first longitudinal inductor L1.

[0089] The free longitudinal inductor L_(F) can always be composed of a longitudinal inductor L or a first longitudinal inductor L₁ and a compensation inductor, which is created by transformation of an additional filter step adjacent to the filter step.

[0090] The result shown in FIG. 4 of the passive transformation can be further transformed corresponding to the transformations of the transverse branch. To this end, after the passive transformation, a parallel transformation is first performed. This transformation is shown in FIG. 5a. The first longitudinal inductors L₁ and the second longitudinal inductors L₂ of the same filter step per longitudinal branch are replaced by a new first longitudinal inductor L₁′ and a new second longitudinal inductor L₂′ such that the new second longitudinal inductor L₂′ is connected in series with resistor R. This series connection is connected in parallel to the new first longitudinal inductor L₁′. In the same filter step the new first longitudinal inductors L₁′ of the first longitudinal branch and the second longitudinal branch are coupled with each other. Furthermore, the new second longitudinal inductors L₂′ of the first longitudinal branch and the second longitudinal branch in the same filter step are coupled with each other.

[0091] To produce a corresponding equivalent circuit diagram relative to the equivalent circuit diagram shown in FIG. 2b, an additional preliminary longitudinal inductor L_(V)′ and an additional compensation inductor L_(K)′ compensating the same are inserted between the above-described parallel connection and the adjacent filter step (see FIG. 5b). The additional compensation inductor L_(K)′ forms at least a portion of the free longitudinal inductor L_(F) of the filter step. The following applies: $L_{K}^{\prime} = \frac{L_{2}^{\prime} \cdot L_{1}^{\prime}}{L_{2}^{\prime} + L_{1}^{\prime}}$

[0092] To perform a first transformation according to FIG. 1a, the additional preliminary longitudinal inductors L_(V)′, the new first longitudinal inductors L₁′ and the new second longitudinal inductors L₂′ are replaced by four end inductors L_(EL)(1), L_(EL)(2), which are coupled with each other, in such a way that an equivalent circuit diagram of the longitudinal end inductors L_(EL)(1), L_(EL)(2) corresponds with a circuit diagram that is formed by the preliminary longitudinal inductors L_(V)′, the new first longitudinal inductors L₁′ and the new second longitudinal inductors L₂′ (see FIG. 6a).

[0093] The first longitudinal end inductor L_(EL)(1) is connected in series with the second end longitudinal inductor L_(EL)(2) to which resistor R of the filter step is connected in parallel. The following applies: ${L_{EL}(1)} = \frac{L_{2}^{\prime}}{L_{2}^{\prime} + L_{1}^{\prime}}$

 L _(EL) (2)=L ₂ ′+L ₁′

[0094] The winding direction of the first longitudinal end inductor L_(EL)(1) relative to a fifth reference point 5 on the electrical connection between the first longitudinal end inductor L_(EL)(1) and the second longitudinal end inductor L_(EL)(2) corresponds with the winding direction of the second end inductor L_(EL)(2) relative to the fifth reference point 5. Here, too, only the relative winding direction is important.

[0095] Starting from the parallel-transformed filter arrangement of FIG. 5b, for example the transformation according to FIG. 1b, i.e., the second transformation, can also be performed. This gives the filter configuration depicted in FIG. 6b. A first longitudinal end inductor L_(EL)(1′) is connected in series with resistor R of the filter step in the first longitudinal branch. A second longitudinal end inductor L_(EL)(2′) is connected in parallel to this series connection. The following applies: ${L_{EL}\left( 1^{\prime} \right)} = \frac{L_{2}^{\prime 2}}{L_{1}^{\prime} + L_{2}^{\prime}}$ ${L_{EL}\left( 2^{\prime} \right)} = \frac{L_{1}^{\prime 2}}{L_{1}^{\prime} + L_{2}^{\prime}}$

[0096] The winding direction of the first longitudinal end inductor L_(EL)(1′) relative to a third reference point 3 on the electrical connection between the first longitudinal end inductor L_(EL)(1′) and the second longitudinal end inductor L_(EL)(2′) is opposite to the winding direction of the second longitudinal end inductor L_(EL)(2′) relative to the third reference point 3. Here, too, only the relative winding direction is important.

[0097] Based on the parallel-transformed filter configuration of FIG. 5b, for example the third transformation according to FIG. 1c can also be performed. A second longitudinal end inductor L_(EL)(2″) and a resistor R are connected in series. An electrical connection is connected in parallel to the series connection comprised of the second longitudinal end inductor L_(EL) (2″) and the resistor R. A first longitudinal end inductor L_(EL)(1″) is connected with the series connection comprised of the second longitudinal end inductor L_(EL)(2″) and the resistor R.

[0098] The following applies:

L _(EL) (1″)=L ₂ ″+L ₁″

L _(EL) (2″)=L ₁″²/(L ₂ ″+L ₁″)

[0099] The winding direction of the first longitudinal end inductor L_(EL)(1″) relative to an eighth reference point 8 on the electrical connection between the first longitudinal end inductor L_(EL)(1′) and the second longitudinal end inductor L_(EL)(2′) corresponds with the winding direction of the second longitudinal end inductor L_(EL)(2″) relative to the eighth reference point 8. Here, too, only the relative winding direction is important.

[0100] Preferably, more than two filter steps are provided.

[0101]FIG. 7 shows a filter arrangement with a first filter step A, a second filter step B and a third filter step C. The transverse branches of the filter arrangement follow from the first transformations. The longitudinal inductors of the second step B and the third step C follow from the second transformations with prior passive transformation and parallel transformation. The longitudinal inductors of the first filter step A have been subjected to a passive transformation to increase the return loss. The values of the inductors, resistors and capacitors are shown in Table 1. The winding directions of the first longitudinal end inductor L_(EL)(1′) and the second longitudinal end inductor L_(EL)(2′) of the second filter step B in the upper longitudinal branch are opposite to each other relative to the third reference point 3. The third reference point 3 lies on the electrical connection between the first longitudinal end inductor L_(EL)(1′) and the second longitudinal end inductor L_(EL)(2′). This is true, correspondingly, for the longitudinal end inductors L_(EL) (1′), L_(EL)(2′) of the third filter step C in the upper longitudinal branch. It is true, correspondingly, for the longitudinal end inductors L_(EL)(1′), L_(EL)(2′) of the second filter step B or the third filter step C in the lower longitudinal branch relative to a fourth reference point 4. TABLE 1 Component Step Value K0 0 6.8 nF L₁ A 763 μH L₂ A 2598 μH 2*R_(T) A 27.5 ohm L_(E)(1) B 5.7 L_(E)(2) B 907 μH K B 11.7 nF L_(EL)(1′) B 235 μH L_(EL)(2′) B 2974 μH 2*R B 51.7 ohm L_(E)(1) C 3.6 μH L_(E)(2) C 462 μH K C 10.5 nF L_(EL)(1′) C 113 μH L_(EL)(2′) C 1569 μH 2*R C 26.7 ohm

[0102]FIG. 8 shows a filter arrangement with a first filter step A′, a second filter step B′ and a third filter step C′ in which the transverse branches follow from a first transformation, the longitudinal inductors of the second step B′ and the third step C′ likewise follow from a first transformation with prior passive transformation and parallel transformation, and the longitudinal inductors of the first step follow from a passive transformation. The values of the inductors, resistors and capacitors are shown in Table 2. The winding direction of the first longitudinal end inductor L_(EL)(1) and the second longitudinal end inductor L_(EL)(2) of the second filter step B′ in the upper longitudinal branch correspond with each other with respect to the fifth reference point 5. The fifth reference point 5 lies on the electrical connection between the first longitudinal end inductor L_(EL)(1) and the second longitudinal end inductor L_(EL)(2). This is true, correspondingly, for the longitudinal end inductors L_(EL)(1), L_(EL)(2) of the third filter step C′ in the upper longitudinal branch. It is true, correspondingly, for the longitudinal end inductors L_(EL)(1), L_(EL)(2) of the second filter step B′ or the third filter step C′ in the lower longitudinal branch relative to a sixth reference point 6. TABLE 2 Component Step Value K0 0 6.8 nF L₁ A′ 763 μH L₂ A′ 2598 μH 2*R A′ 27.5 ohm L_(E)(1) B′ 5.7 μH L_(E)(2) B′ 907 μH K B′ 11.7 nF L_(EL)(1) B′ 235 μH L_(EL)(2) B′ 4881 μH 2*R B′ 51.7 ohm L_(E)(1) C′ 3.6 μH L_(E)(2) C′ 462 μH K C′ 10.5 nF L_(EL)(1) C′ 113 μH L_(EL)(2) C′ 2524 μH 2*R C, 26.7 ohm

[0103] It is also within the scope of the invention not to transform all of the inductors and not to transform all of the filter steps.

[0104] It is within the scope of the invention to subject different transverse branches of the same filter arrangement to different transformations. The same applies to the longitudinal inductors.

[0105]FIG. 9 shows a filter system with a first filter step A″, a second filter step B″ and a third filter step C″, in which the transverse branch of the second filter step B″ and the longitudinal inductors of the third filter step C″ follow from a first transformation, and the transverse branch of the third filter step C″ and the longitudinal inductors of the second filter step B″ follow from a second transformation. The longitudinal inductors were previously subjected to a passive transformation and a parallel transformation. The longitudinal inductors of the first step follow from a passive transformation. The values of the inductors, resistors and capacitors are shown in Table 3. The winding directions of the first end inductor L_(E)(1′) and the second end inductor L_(E)(2′) of the third filter step C″ in the upper longitudinal branch are opposite to each other relative to the first reference point 1. The first reference point 1 lies on the electrical connection between the first end inductor L_(E)(1′) and the second end inductor L_(E)(2′). This is true, correspondingly, for the respective end inductors L_(E)(1′), L_(E)(2′) in the lower longitudinal branch relative to a second reference point 2. TABLE 3 Component Step Value K0 0 6.8 nF L₁ A″ 763 μH L₂ A″ 2598 μH 2*R A″ 27.5 ohm L_(E)(1) B″ 5.7 μH L_(E)(2) B″ 907 μH K B″ 11.7 nF L_(EL)(1′) B″ 235 μH L_(EL)(2′) B″ 2974 μH 2*R B″ 51.7 ohm L_(E)(1′) C″ 384 μH L_(E)(2′) C″ 3.6 μH K C″ 10.5 nF L_(EL)(1) C″ 113 μH L_(EL)(2) C″ 2524 μH 2*R C″ 26.7 ohm

[0106]FIG. 10 shows a filter arrangement with a first filter step A′″, a second filter step B′″ and a third filter step C′″, in which the transverse branch of the second filter step B′″ follows from a first transformation, and the transverse branch of the third filter step C′″ follows from a second transformation. The longitudinal inductors of all three filter steps A′″, B′″, C′″ follow from a passive transformation. The values of the inductors, resistors and capacitors are shown in Table 4. TABLE 4 Component Step Value K0 0 6.8 nF L₁ A″′ 763 μH L₂ A″′ 2598 μH 2*R A″′ 27.5 ohm L_(E)(1) B″′ 5.7 μH L_(E)(2) B″′ 907 μH K B″′ 11.7 nF L₂ B″′ 2974 μH 2*R B″′ 31.5 ohm L_(E)(1′) C″′ 384 μH L_(E)(2′) C″′ 3.6 μH K C″′ 10.5 nF L₂ C″′ 1569 μH 2*R C″′ 16.6 ohm

[0107]FIG. 11 shows a filter system with a first filter step A″″, a second filter step B″″ and a third filter step C″″, in which the transverse branch of the second filter step B″″ follows from a first transformation, and the transverse branch of the third filter step C″″ follows from a second transformation. The longitudinal inductors of the second filter step B″″ follow from a passive transformation, a parallel transformation and a subsequent second transformation. The longitudinal inductors of the first filter step A″″ and the third filter step C″″ were not transformed. The values of the inductors, resistors and capacitors are shown in Table 5. TABLE 5 Component Step Value K0 0 6.8 nF L 1 1016.3 μH L_(E)(1) 2 5.7 μH L_(E)(2) 2 907 μH K 2 11.7 nF L_(EL)(1′) 2 2974 μH L_(EL)(2′) 2 235.1 μH 2*R 2 51.7 ohm L_(E)(1′) 3 535.6 μH L_(E)(2′) 3 2.74 μH K 3 10.5 nF

[0108] When calculating the values of the inductors, it is recommended, prior to transformation of the filter step, first to transform an additional filter step adjacent to the filter step, whose transverse branch directly adjoins the filter step, and subsequently to transform the filter step. In this way, the compensation inductor inserted in the transformation of the additional adjacent filter step can be integrated into the free longitudinal inductor of the filter step and taken into account immediately in the transformation of the filter step. 

1. Method for designing a filter system with at least two longitudinal branches having longitudinal inductors, at least one filter step (B), which has at least one transverse branch interposed between the longitudinal branches, and at least one adjacent filter step (A), which directly adjoins the transverse branch, wherein the configuration of the inductors is determined by means of transformation by the following process steps: first, the filter step (B) has at least one free longitudinal inductor (L_(K)′) of the first longitudinal branch, a free longitudinal inductor of the second longitudinal branch coupled therewith and the transverse branch, which consists of a capacitor (K) that is interposed between two transverse inductors (L_(Q)) coupled with each other, and first the adjacent filter step (A) has at least one free longitudinal inductor (L_(K)′) of the first longitudinal branch and a free longitudinal inductor of the second longitudinal branch coupled therewith, subsequently, in each longitudinal branch between the transverse branch and the adjacent filter step (A) a preliminary longitudinal inductor (L_(V)) and a compensating inductor (L_(K)) compensating the same and connected in series therewith are inserted, wherein the preliminary longitudinal inductors (L_(V)) are coupled with each other and the compensation inductors (L_(K)) are coupled with each other, subsequently, the compensation inductors (L_(K)) are integrated into the free longitudinal inductors (L₁) of the adjacent filter step (A), subsequently, the preliminary longitudinal inductors (L_(V)), the free longitudinal inductors (L_(K)′) of the filter step (B) and the transverse inductors (L_(Q)) are replaced by four end inductors (L_(E)(1), L_(E)(2) that are coupled with each other such that an equivalent circuit diagram of the four end inductors (L_(E)(1), L_(E)(2) corresponds with the circuit diagram of the preliminary longitudinal inductors (L_(V)), the free longitudinal inductors (L_(K)′) of the filter step (B) and the transverse inductors (L_(Q)).
 2. Method for designing a filter system with at least two longitudinal branches having longitudinal inductors, at least one filter step (B), which has at least one transverse branch interposed between the longitudinal branches, and at least one adjacent filter step (A), which directly adjoins the transverse branch, wherein the configuration of the inductors is determined by means of transformation by the following process steps: first, the filter step (B′″) has a longitudinal inductor (L) of the first longitudinal branch, a longitudinal inductor of the second longitudinal branch coupled therewith and the transverse branch, and the adjacent filter step (A′″) first has at least one longitudinal inductor (L) of the first longitudinal branch and a longitudinal inductor of the second longitudinal branch coupled therewith, subsequently, the longitudinal inductors (L) of the filter step (B′″) are replaced, respectively, by a first longitudinal inductor (L₁), which forms at least a portion of the free longitudinal inductor, and a second longitudinal inductor (L₂) connected in series therewith, to which a resistor R is connected in parallel, wherein corresponding longitudinal inductors that belong to the same filter step are coupled with each other, and subsequently, the preliminary longitudinal inductor (L_(V)) and the compensation inductor (L_(K)) are inserted.
 3. Method for designing a filter system with at least two longitudinal branches having longitudinal inductors, at least one filter step (B), which has at least one transverse branch interposed between the longitudinal branches, and at least one adjacent filter step (A), which directly adjoins the transverse branch, wherein the configuration of the inductors is determined by means of transformation by the following process steps: first, the filter step (B) has a longitudinal inductor (L) of the first longitudinal branch, a longitudinal inductor of the second longitudinal branch coupled therewith and the transverse branch, and the adjacent filter step (A) first has at least one longitudinal inductor (L) of the first longitudinal branch and a longitudinal inductor of the second longitudinal branch coupled therewith, subsequently, the longitudinal inductors (L) of the filter step (B) and the adjacent filter step are replaced, respectively, by a first longitudinal inductor (L₁) and a second longitudinal inductor (L₂) connected in series therewith, to which a resistor (R) is connected in parallel, wherein corresponding longitudinal inductors that belong to the same filter step are coupled with each other, subsequently, the first longitudinal inductors (L₁) and the second longitudinal inductors (L₂) of the same filter step per longitudinal branch are replaced by a new first longitudinal inductor (L₁′) and a new second longitudinal inductor (L₂′) such that the new second longitudinal inductor (L₂′) is connected in series with the resistor (R), said series connection is connected in parallel to the new first longitudinal inductor (L₁′), in the same filter step the new first longitudinal inductors (L₁′) of the first longitudinal branch and the second longitudinal branch are coupled with each other and the new second longitudinal inductors (L₂′) of the first longitudinal branch and the second longitudinal branch are coupled with each other, subsequently, in each longitudinal branch of the filter step (B) an additional preliminary longitudinal inductor (L_(V)′) and an additional compensation inductor (L_(K)′) compensating the same and forming at least a portion of the free longitudinal inductor, are inserted between the parallel connection of the new first longitudinal inductor (L₁′) to the series connection and the adjacent filter step (A), subsequently, the additional preliminary longitudinal inductors (L_(V)′), the new first longitudinal inductors (L₂′), which form an additional circuit diagram, are replaced by four longitudinal end inductors L_(E)(1′), L_(E)(2′) that are coupled with each other, such that an equivalent circuit diagram of the four longitudinal end inductors (L_(E)(1′), L_(E)(2′) corresponds with the additional circuit diagram, and subsequently, the preliminary longitudinal inductor (L_(V)) and the compensation inductor (L_(K)) are inserted.
 4. Method as claimed in any one of claims 1 to 3, in which a first capacitor electrode of the capacitor (K) is connected with a first end inductor (L_(E)(1)) that is connected with the adjacent filter step (A) and with a second end inductor (L_(E)(2)), in which the winding direction of the first end inductor (L_(E)(1)) relative to the capacitor (K) corresponds with the winding direction of the second end inductor (L_(E)(2)) relative to the capacitor (K), in which a second capacitor electrode of the capacitor is connected with a third end inductor (L_(E)(1)) that is connected with the adjacent filter step (A) and with a fourth end inductor (L_(E)(2)), in which the winding direction of the first end inductor (L_(E)(1)) relative to the capacitor (K) is opposite to the winding direction of the third end inductor (L_(E)(1)) relative to the capacitor (K), in which the winding direction of the third end inductor (L_(E)(1)) relative to the capacitor (K) corresponds with the winding direction of the fourth end inductor (L_(E)(2)) relative to the capacitor (K).
 5. Method as claimed in any one of claims 1 to 3, in which a first capacitor electrode of the capacitor (K) is connected with a first end inductor (L_(E)(1′)), which is connected with the adjacent filter step (B″), in which a second end inductor (L_(E)(2′)) is connected with the first end inductor (L_(E)(1′)) and with the adjacent filter step (B″), in which the winding direction of the first end inductor (L_(E)(1′)) relative to a first reference point (1) on the electrical connection between the first end inductor (L_(E)(1′)) and the second end inductor (L_(E)(2′)) is opposite to the winding direction of the second end inductor relative to the first reference point (1), in which a second capacitor electrode of the capacitor (K) is connected with a third end inductor (L_(E)(1′)), which is connected with the adjacent filter step (B″), in which a fourth end inductor (L_(E)(2′)) is connected with the third end inductor (L_(E)(1′)) and with the adjacent filter step (B″), in which the winding direction of the third end inductor (L_(E)(1′)) relative to a second reference point (2) on the electrical connection between the third end inductor (L_(E)(1′)) and the fourth end inductor (L_(E)(2′)) is opposite to the winding direction of the fourth end inductor (L_(E)(2′)) relative to the second reference point (2), in which the winding direction of the first end inductor (L_(E)(1′)) relative to the capacitor (K) is opposite to the winding direction of the third end inductor (L_(E)(1′)) relative to the capacitor (K).
 6. Method as claimed in any one of claims 1 to 3, in which a first capacitor electrode of the capacitor (K) is connected with a second end inductor (L_(E)(2′)), in which the second end inductor (L_(E)(2″)) is connected with a first end inductor (L_(E)(1″)), which is connected with the adjacent filter step, in which the winding direction of the first end inductor (L_(E)(1″)) relative to a seventh reference point (7) on the electrical connection between the first end inductor (L_(E)(1″)) and the second end inductor (L_(E)(2″)) is opposite to the winding direction of the second end inductor (L_(E)(2″)) relative to the seventh reference point (7), in which a second capacitor electrode of the capacitor (K) is connected with a fourth end inductor, in which the fourth end inductor is connected with a third end inductor that is connected with the adjacent filter step, in which the winding direction of the third end inductor relative to a ninth reference point on the electrical connection between the third end inductor and the fourth end inductor is opposite to the winding direction of the fourth end inductor relative to the ninth reference point, in which the winding direction of the first end inductor (L_(E)(1″)) relative to the capacitor (K) is opposite to the winding direction of the third end inductor relative to the capacitor (K).
 7. Method as claimed in any one of claims 3 to 6, in which a first longitudinal end inductor (L_(EL)(1′)) is connected in series with the resistor (R) of the filter step (B) in the first longitudinal branch, and a second longitudinal end inductor (L_(EL)(2′)) is connected in parallel to said series connection, in which the winding direction of the first longitudinal end inductor (L_(EL)(1′)) relative to a third reference point (3) on the electrical connection between the first longitudinal end inductor (L_(EL)(1′)) and the second longitudinal end inductor (L_(EL)(2′) is opposite to the winding direction of the second longitudinal end inductor (L_(EL)(2′)) relative to the third reference point (3), in which a third longitudinal end inductor (L_(EL)(1′)) is connected in series with the resistor R of the filter step (B) in the second longitudinal branch, and a fourth longitudinal end inductor (L_(EL)(2′)) is connected in parallel to said series connection, in which the winding direction of the third longitudinal end inductor (L_(EL)(1′)) relative to a fourth reference point (4) on the electrical connection is between the third longitudinal end inductor (L_(EL)(1′)) and the fourth longitudinal end inductor (L_(EL)(2′)) relative to the fourth reference point (4), in which the winding direction of the first longitudinal end inductor (L_(EL)(1′)) relative to the transverse branch is opposite to the winding direction of the third longitudinal end inductor (L_(E)(1′)) relative to the transverse branch.
 8. Method as claimed in any one of claims 3 to 6, in which a first longitudinal end inductor (L_(EL)(1)) is connected in series with a second longitudinal end inductor (L_(EL)(2)), to which the resistor R of the filter step (B′) in the first longitudinal branch is connected in parallel, in which the winding direction of the first longitudinal end inductor (L_(EL)(1)) relative to a fifth reference point (5) on the electrical connection between the first longitudinal end inductor (L_(EL)(1)) and the second longitudinal end inductor (L_(EL)(2)) corresponds with the winding direction of the second longitudinal end inductor (L_(EL)(2)) relative to the fifth reference point (5), in which a third longitudinal end inductor (L_(EL)(1)) with a fourth longitudinal end inductor (L_(EL)(2)) to which the resistor (R) of the filter step (B) in the second longitudinal branch is connected in parallel, in which the winding direction of the third longitudinal end inductor (L_(EL)(1)) relative to a sixth reference point (6) on the electrical connection between the third longitudinal end inductor (L_(EL)(1)) and the fourth longitudinal end inductor (L_(EL)(2)) corresponds with the winding direction of the fourth longitudinal end inductor (L_(EL)(2)) relative to the sixth reference point (6), in which the winding direction of the first longitudinal end inductor (L_(EL)(1)) relative to the transverse branch is opposite to the winding direction of the third longitudinal end inductor (L_(E)(1)) relative to the transverse branch.
 9. Method as claimed in any one of claims 3 to 6, in which a second longitudinal end inductor (L_(EL)(2″)) and a resistor (R) of the filter step in the first longitudinal branch are connected in series, in which an electrical connection is connected in parallel to the series connection comprised of the second longitudinal end inductor (L_(EL)(2″) and the resistor (R), in which a first longitudinal end inductor (L_(EL)(1″)) is interposed between the adjacent filter step and the series connection comprised of the second longitudinal end inductor (L_(EL)(2″)) and the resistor (R), in which the winding direction of the first longitudinal end inductor (L_(EL)(1″)) relative to an eighth reference point (8) on the electrical connection between the first longitudinal end inductor (L_(EL)(1″)) and the second longitudinal end inductor (L_(EL)(2″)) corresponds with the winding direction of the second longitudinal end inductor (L_(EL)(2″)) relative to the eighth reference point (8), in which a fourth longitudinal end inductor and a resistor of the filter step in the first longitudinal branch are connected in series, in which an electrical connection is connected in parallel to the series connection comprised of the fourth longitudinal end inductor and the resistor, in which a third longitudinal end inductor is interposed between the adjacent filter step and the series connection comprised of the fourth longitudinal end inductor and the resistor, in which the winding direction of the third longitudinal end inductor relative to a tenth reference point on the electrical connection between the third longitudinal end inductor and the fourth longitudinal end inductor corresponds with the winding direction of the fourth longitudinal end inductor relative to the tenth reference point, in which the winding direction of the first longitudinal end inductor (L_(EL)(1″)) relative to the transverse branch is opposite to the winding direction of the third longitudinal end inductor relative to the transverse branch.
 10. Method as claimed in any one of claims 1 to 9, in which at least one additional filter step (C) is provided adjacent to filter step (B), in which the compensation inductor (L_(K)) for the transformation of the additional adjacent filter step (C) are integrated into the free longitudinal inductors (L_(K)′) of the filter step (B). 